Strictly correlated uniform electron droplets

TL;DR

This paper investigates the energetic properties of finite, uniform electron droplets in various dimensions under strict correlation, providing data that aids the development of density functional theory and testing bounds on electron interactions.

Contribution

It offers new insights into the behavior of strongly correlated electron droplets and verifies the Lieb-Oxford bound across different dimensions and interaction types.

Findings

Coulomb interaction increases with electron number.

Lieb-Oxford bound is satisfied in all studied dimensions.

Bound is exactly reached in 1D droplets.

Abstract

We study the energetic properties of finite but internally homogeneous D-dimensional electron droplets in the strict-correlation limit. The indirect Coulomb interaction is found to increase as a function of the electron number, approaching the tighter forms of the Lieb-Oxford bound recently proposed by Rasanen et al. [Phys. Rev. Lett. 102, 206406 (2009)]. The bound is satisfied in three-, two-, and one-dimensional droplets, and in the latter case it is reached exactly - regardless of the type of interaction considered. Our results provide useful reference data for delocalized strongly correlated systems, and they can be used in the development and testing of exchange-correlation density functionals in the framework of density-functional theory.